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Exercise E
14. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
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15.
Find the mean salary of 60 workers of a factory from the following table:
Salary (Rs) Number of workers 3000 16 4000 12 5000 10 6000 8 7000 6 8000 4 9000 3 10000 1 Total 60
16.
100 surnames were randomly picked up from a local telephone directory and frequency
distributions of the number of letters in the English alphabet in the surnames was ound as
follows:
Number of letters Number of surnames 1 – 4 6 4 – 6 30 6 – 8 44 8 – 12 16
12 – 20
4 (i)
Draw a histogram to depict the given information.
(ii)
Write the class interval in which the maximum number if surnames lie.
17.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data
18.
A family with a monthly income of Rs 20,000 had planned the following expenditures per month
under various heads: Draw a bar graph for the given below data.
19.
The value of upto 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510 (i) Make a frequency
distribution of the digits from 0 to 9 after the decimal point. (ii) What are the most and the least
frequently occurring digits?
20.
The following observations have been arranged in ascending order as 29, 32, 48, 50, x, x + 2, 72,
78, 84, 95. If the median of the data is 63, find the value of x.
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21. Consider the marks, out of 100, obtained by 51 students of a class in a test, given in below table.
Draw a frequency polygon corresponding to this frequency distribution table.
22.
In a city, the weekly observations made in a study on the cost of living index are given below in
the following table: Draw a frequency polygon for the data abo e (without constructing a
histogram).
23. The following table gives the life times of 400 neon lamps: (i) Represent the given information
with the help of a histogram. (ii) How many lamps have a life time of more than 700 hours?
Life time (in hours) Number of lamps 300 – 400 14 400 – 500 56 500 – 600 60 600 – 700 86 700 – 800 74 800 – 900
62
900 – 1000 48
24. The mean of 13 observations is 14. If the mean of the first 7 observations is 12 and that of last 7
observation is 16, find the 7th observation.
25. The average monthly salary of 15 workers in a factory is Rs. 285. If the salary of the manager is
included, the average becomes Rs. 355. What is the manager’s salary?
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26.
For what value of x, is the mode of the following data is 17?
15, 16, 17, 14, 17 16, 13, x, 17, 16, 15, 15
27.
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
Represent the data of both the teams on the same graph by frequency polygons.
28.
A random survey of the number of children of various age groups playing in a park was found as
follows: Draw a histogram to represent the data above.
Age(in years) Number of children 1 – 2 5 2 – 3 3 3 – 5 6 5 – 7 12 7 – 10 9
10 – 15
10 15 – 17 4
29.
Calculate mean (by using assume mean method), median and mode.
Income 50 150 250 350 450 550 650 750 No. of persons 4 8 9 10 7 5 4 3
30.
The mean of the following distribution is 107. Find the value of f1 and f2.
x 15 45 75 105 135 165 195 Total f 2 3 f1 10 3 f2 2 30
31.
Find the median of the distribution obtained in question no.2.
32.
Find the median of first sixteen odd numbers.
33.
Find the median of first ten prime numbers.
34.
A school has two sections. The mean mark of one section of size 40 is 60 and mean mark of
other section of size 60 is 80. Find the combined mean of all the students of the school.
35.
The median of the following observations arranged in ascending order 8, 9, 12, 18, (x + 2), (x +
4), 30, 31, 34, 39 is 24. Find x.
36.
The mean weight of 180 students in a school is 50kg. The mean weight of boys is 60kg while
that of the girls is 45kg. Find the number of the boys and girls in the school.
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37. Draw histogram and frequency polygon for the following distribution:
C. I. 0 – 50 50 – 100 100 – 150 150 – 200 200 – 250 250 – 300 F 4 8 16 13 6 3
38. Calculate mean by step deviation method:
Marks 5.5 15.5 25.5 35.5 45.5 55.5 No. of Students 3 16 26 31 16 8
39. The mean of the following distribution is 15. Find the value of a.
C. I. 5 10 15 20 25 Freq 6 a 6 10 5
40. Calculate mean by step deviation method:
Marks 15 25 35 45 55 No. of Students 20 24 40 36 20
41. The mean of the following distribution is 50. Find the value of p.
C. I. 10 30 50 70 90 Freq 17 p 32 24 19
42. Find the missing frequencies from the frequency distribution if he mean is 472 for 100 workers
Income 250 350 450 550 650 750 850 No. of workers 5 x y 16 9 6 4
43. In a school 90 boys and 30 girls appeared in a public examination. The mean marks of boys was
found to be 45% whereas the mean marks of girls was 70%. Determine the average marks % of the school.
44. The marks secured by 15 students are 70, 55, 95, 62, 82, 65, 60, 68, 75, 58, 64, 85, 80, 90, 51.
Find the median marks.
45. Calculate mean (by using short cut method), median and mode.
Marks 25 35 45 55 65 75 85 95 No. of Students 5 12 6 20 18 10 16 3
46. The mean of the following distribution is 112.2 for the sum of observation 100. Find the value of x and y.
C I. 60 80 100 120 140 160 Freq 18 X 13 27 Y 22
47. The median of the following observations arranged in ascending order 8, 9, 12, 18, (x + 2), (x +
4), 30, 31, 34, 39 is 24. Find x.
48. If the mean of 2x + 3, 3x + 4, x + 7, x – 3, 4x – 7 is 14. Find the value of x.
49. The mean of 8 numbers is 15. If each number if multiplied by 2, what will be the new mean?
50. Find the mean (by using assume mean method), median and mode of the following distribution:
x 15 25 35 45 55 65 f 90 50 60 80 50 30
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51.
Find the mean (by using step deviation method) ,median and mode of the given data:
x 6 10 14 18 22 26 30 f 2 4 7 12 8 4 3
52.
Draw histogram and frequency polygon for the following data:
Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 No. of students 10 12 13 11 9
53.
The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the
last 13 observations is 39, find the 13th observation.
54.
Find mean (by using assume mean method), median and mode of the following table:
Salaries (in Rs.) 1500 2000 2500 3000 3500 4000 4500 5000 No. of workers 16 12 10 8 6 4 3 1
55.
Find the mean (by using step deviation method), median and mode of the following distribution:
x 24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5 f 5 12 15 20 18 10 6 4
56.
For the following data, draw a histogram and a frequency polygon
Marks 20-30
30-40
40-50
50-60
60-70
70 80
80-90
90-100
No. of students 5 12 6 20 18 10 16 3
57.
Given below are the ages of 25 students of class IX n a school.
Prepare a discrete frequency distribution table.
15 16 16 17 17 16 15 15 16 16 17 15 16 16 14 16 15 14 15 16 16 15 14 14 15
58.
Find the median of the following data: 33, 31, 48, 45, 41, 92, 78, 51, and 61. If 92 is replaced by
29, what will be the new median?
59.
Following are the marks of a group of students in a test of reading ability test:
Marks: 50 – 52 47 – 49 44 – 46 41 – 43 38 – 40 35 – 37 32 – 34 Total No. of students 4 10 15 18 20 12 13 92 Construct a histogram and frequency polygon for the above data.
60.
For the following data, draw a histogram and a frequency polygon
x 0 – 10
10 – 20 20 – 30 30 – 50 50 – 60 60 – 80 80 – 90 90 –100 f 5 12 15 20 18 10 6 4
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